arXiv research

The Internet has rich and rapidly increasing sources of high quality educational content. Inferring prerequisite relations between educational concepts is required for modern large-scale online educational technology applications such as personalized recommendations and automatic curriculum creation. We present PREREQ,…

MCD offers a complete model understanding for high-stake decisions.

Study connects isoperimetric sets, mass concepts, and nonnegative scalar curvature.

This review covers learning under concept drift, including detection, understanding, and adaptation.

System helps engineers with concept recognition for SEVA.

Paper discusses the Fisher metric and differentiability in statistical models.

Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a dedicated formalism. In this paper, we generalize graph concepts in order to cope with…

Strict partial order is a mathematical structure commonly seen in relational data. One obstacle to extracting such type of relations at scale is the lack of large-scale labels for building effective data-driven solutions. We develop an active learning framework for mining such relations subject to a strict order. Our a…

The paper reviews and extends calibration concepts for classification and regression.

This paper (the seventh paper in a series of eight) continues the development of our theory of multivector and extensor calculus on smooth manifolds. Here we deal first with the concepts of ordinary Hodge coderivatives, duality identities, and Hodge coderivative identities. Then, we recall the concept of a Levi-Civita …

Explanations for deep neural network predictions in terms of domain-related concepts can be valuable in medical applications, where justifications are important for confidence in the decision-making. In this work, we propose a methodology to exploit continuous concept measures as Regression Concept Vectors (RCVs) in th…

Using different sources of information to support automated extracting of relations between biomedical concepts contributes to the development of our understanding of biological systems. The primary comprehensive source of these relations is biomedical literature. Several relation extraction approaches have been propos…

Asymptotic net is an important concept in discrete differential geometry. In this paper, we show that we can associate affine discrete geometric concepts to an arbitrary non-degenerate asymptotic net. These concepts include discrete affine area, mean curvature, normal and co-normal vector fields and cubic form, and the…

Introduces Relational Privacy (RP) to control relation memorization in question answering models.

Study challenges neural models in compositional learning tasks.

The study identifies latent concepts from diverse observations without assuming specific models.

Service robots benefit from encoding information in semantically meaningful ways to enable more robust task execution. Prior work has shown multi-relational embeddings can encode semantic knowledge graphs to promote generalizability and scalability, but only within a batched learning paradigm. We present Incremental Se…

Analogously to the concept of a curvature of curve and surface, in the differential geometry, in the main part of this paper the concept of the curvature of the hyper-dimensional vector spaces of Riemannian metric is generally defined. The defined concept of the curvature of Riemannian spaces of higher dimensions M: M>…

In this review paper we discuss the different interpretations of the concept of connection in a fiber bundle and in a jet bundle, and relate it with first and second-order systems of partial differential equations (PDE's) and multivector fields. As particular cases we analyze the concepts of linear connections and conn…

Extends linear representation hypothesis to categorical and hierarchical concepts in LLMs.

Improves medical note processing by training model on related concepts and global context.

We study the concept of the fourth skein module of 3-manifolds, that is a skein module based on the skein relation b_0L_0 + b_1L_1 + b_2L_2 + b_3L_3 = 0 and a framing relation L^{(1)} = aL, where a, b_0, b_3 are invertible. We introdule the concept of n-algebraic tangles (and links) and analyze the skein module for 3-a…

VCML learns concepts and metaconcepts from images and questions.

HCBM improves deep learning explainability by non-linear concept aggregation.

Unified approach to learn interpretable concepts from data.

A new framework for interpretable models using sparse linear layers.

We prove that "generalized Lie algebroid", a geometric object which appeared recently in the literature, is a misconception.

This paper focuses on a traditional relation extraction task in the context of limited annotated data and a narrow knowledge domain. We explore this task with a clinical corpus consisting of 200 breast cancer follow-up treatment letters in which 16 distinct types of relations are annotated. We experiment with an approa…

Deep learning skin lesion classifier explained using CAVs.

Introduces $k$-slant distributions and submanifolds in various geometric settings.

Uniformity and proximity are two different ways for defining small scale structures on a set. Coarse structures are large scale counterparts of uniform structures. In this paper, motivated by the definition of proximity, we develop the concept of asymptotic resemblance as a relation between subsets of a set to define a…

We introduce the concept of tied links in the solid torus, which generalize naturally the concept of tied links in $S^3$ previously introduced by Aicardi and Juyumaya. We also define an invariant of these tied links by using skein relations, and subsequently we recover this invariant by using Jones' method over the bt-…

Teaching models for concept learning infer concepts from observations.

Economic systems are similar with physic systems for their large number of individuals and the exist of equilibrium. In this paper, we present a model applying the equilibrium statistical model in economic systems. Consistent with statistical physics, we define a series of concepts, such as economic temperature, econom…

The paper connects higher order risk measures and stochastic dominance, showing their equivalence and integrating them with optimization.

The concept of pure spinor is generalized, giving rise to the notion of pure subspaces, spinorial subspaces associated to isotropic vector subspaces of non-maximal dimension. Several algebraic identities concerning the pure subspaces are proved here, as well as some differential results. Furthermore, the freedom in the…

Concept Relation Discovery and Innovation Enabling Technology (CORDIET), is a toolbox for gaining new knowledge from unstructured text data. At the core of CORDIET is the C-K theory which captures the essential elements of innovation. The tool uses Formal Concept Analysis (FCA), Emergent Self Organizing Maps (ESOM) and…

We introduce the notions of overcommutation and overcommutation length in groups, and show that these concepts are closely related to representations of the fundamental groups of 3-manifold and their Heegaard genus. We give many examples including translations in the affine group of the line and provide upper bounds fo…

With the increasing number of deep learning applications, there is a growing demand for explanations. Visual explanations provide information about which parts of an image are relevant for a classifier's decision. However, highlighting of image parts (e.g., an eye) cannot capture the relevance of a specific feature val…

Study uses crochet to visualize non-Euclidean geometry.

Lifted Relational Neural Networks (LRNNs) describe relational domains using weighted first-order rules which act as templates for constructing feed-forward neural networks. While previous work has shown that using LRNNs can lead to state-of-the-art results in various ILP tasks, these results depended on hand-crafted ru…

In this work, we present an interesting attempt on mixture generation: absorbing different image concepts (e.g., content and style) from different domains and thus generating a new domain with learned concepts. In particular, we propose a mixture generative adversarial network (MIXGAN). MIXGAN learns concepts of conten…

Formalizes concepts as latent variables in hierarchical models for high-dimensional data.

Over 50 million scholarly articles have been published: they constitute a unique repository of knowledge. In particular, one may infer from them relations between scientific concepts, such as synonyms and hyponyms. Artificial neural networks have been recently explored for relation extraction. In this work, we continue…

This paper is a tutorial on Formal Concept Analysis (FCA) and its applications. FCA is an applied branch of Lattice Theory, a mathematical discipline which enables formalisation of concepts as basic units of human thinking and analysing data in the object-attribute form. Originated in early 80s, during the last three d…

We introduce the anisotropic tensor calculus, which is a way of handling with tensors that depend on the direction remaining always in the same class. This means that the derivative of an anisotropic tensor is a tensor of the same type. As an application, we show how to define derivations using anisotropic linear conne…

This paper derives -- considering a Gaussian setting -- closed form solutions of the statistics that Adrian and Brunnermeier and Acharya et al. have suggested as measures of systemic risk to be attached to individual banks. The statistics equal the product of statistic specific Beta-coefficients with the mean corrected…

Concept modulation models unify identifiability and extrapolation in conditional latent variable models.